Lab 4. Data types in Scala

Objectives:

• get familiar with algebraic data types
• get familiar with pattern matching and recursion with them

Given the following implementation of the natural numbers, solve the next few exercices.

trait NaturalNumber
case object Zero extends NaturalNumber
case class Successor(x: NaturalNumber) extends NaturalNumber

4.1.1 Write a function which takes two natural numbers, and return their sum.

def add(x: NaturalNumber, y: NaturalNumber): NaturalNumber = ???

4.1.2 Write a function which takes two natural numbers, and return their product.

def multiply(x: NaturalNumber, y: NaturalNumber): NaturalNumber = ???

4.1.3 Write a function which takes an int and converts it to a NaturalNumber.

def toNaturalNumber(x: Int): NaturalNumber = ???

Given the following implementation of binary trees, solve the next few exercices.

trait BTree
case object EmptyTree extends BTree
case class Node(value: Int, left: BTree, right: BTree) extends BTree

4.2.1 Write a function which takes a BinaryTree and returns its depth.

def depth(tree: BTree): Int = ???

4.2.2 Write a function which takes a BinaryTree and returns the number of nodes with even number of children.

def evenChildCount(tree: BTree): Int = ???

4.2.3 Write a function which takes a BinaryTree and flattens it (turns it into a list containing the values of the nodes).

def flatten(tree: BTree): List[Int] = ???

4.2.4 Write a function which takes a BinaryTree and return the number of nodes whose values follow a ceratain rule.

def countNodes(tree: BTree, cond: Int => Boolean): Int = ???

4.2.5 Write a function which takes a BinaryTree and return mirrored BTree.

def mirror(tree: BTree): BTree= ???

Given the following implementation of a generalized matrix, solve the next few exercices.

trait GMatrix
case class Scalar(value: Int) extends GMatrix
case class Vector(values: List[Int]) extends GMatrix
case class Matrix(values: List[List[Int]]) extends GMatrix

4.3.1 Write a function which takes a GMatrix and multiplies each element by an Int.

def multiply(m: GMatrix, x: Int): GMatrix = ???

4.3.1 Write a function which takes a two GMatrices and multiplies them

def multiply(m1: GMatrix, m2: GMatrix): GMatrix = ???

Given the following implementation of a human genome, solve the next few exercices.

trait Gene
case class A(code: Int) extends Gene
case class C(code: Int) extends Gene
case class G(code: Int) extends Gene
case class T(code: Int) extends Gene

4.4.1 Write a function which takes a two gene sequencies and checks their compatibility. A-T, C-G, T-A, G-C

def compatibility(seq1: List[Gene], seq2: List[Gene]): Boolean = ???

4.4.2 Write a function which takes a gene sequence and checks their encoded value (G1G2G3 → code1code2code3)

def encode(seq: List[Gene]): List[Int]= ???

4.4.2 Write a function which takes a gene sequence and returns the gene sequence that annihilates given one (make the wrong combinations, unlike 4.4.1)

def worstEnemy(seq: List[Gene]): List[Gene]= ???